Can an employee drop their health insurance coverage when it isn't their open enrollment to join their spouses coverage at their spouses open enrollment?

You can but it is unwise because you need to know when you would be covered by the spouse's health plan. Some plans have 3 and 6 monthj waiting periods. So it is wise to keep your insurance, sign up on the spouse's insurance then later on after you have your new coverage in effect you could drop your employer's plan. Some employers however "require" their employees to be covered or are paying for the coverage. Check with your employer about that. Some employers will also refuse to cover you again if you lose your husband's coverage.

If the marriage is not is good shape it is a foolish to drop your own coverage in case there is a divorce. Sorry to mention it but is true.